#define _CRT_SECURE_NO_WARNINGS 1
#include <vector>
using namespace std;

class Solution {
public:
    int uniquePaths(int m, int n)
    {
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));

        dp[0][1] = 1;

        for (int i = 1; i <= m; ++i)
        {
            for (int j = 1; j <= n; ++j)
            {
                dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
            }
        }
        return dp[m][n];
    }
};

class Solution {
public:
    int uniquePathsWithObstacles(vector<vector<int>>& obstacleGrid)
    {
        int m = obstacleGrid.size();
        int n = obstacleGrid[0].size();
        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
        dp[0][1] = 1;

        for (int i = 1; i <= m; ++i)
        {
            for (int j = 1; j <= n; ++j)
            {
                if (obstacleGrid[i - 1][j - 1] == 0)
                {
                    dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
                }
            }
        }
        return dp[m][n];
    }
};

class Solution {
public:
    int jewelleryValue(vector<vector<int>>& frame)
    {
        int m = frame.size();
        int n = frame[0].size();

        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));

        for (int i = 1; i <= m; ++i)
        {
            for (int j = 1; j <= n; ++j)
            {
                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]) + frame[i - 1][j - 1];
            }
        }
        return dp[m][n];
    }
};

class Solution {
public:
    int minPathSum(vector<vector<int>>& grid)
    {
        int m = grid.size();
        int n = grid[0].size();

        vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0x3f3f3f3f));
        dp[0][1] = 0;

        for (int i = 1; i <= m; ++i)
        {
            for (int j = 1; j <= n; ++j)
            {
                dp[i][j] = min(dp[i - 1][j], dp[i][j - 1]) + grid[i - 1][j - 1];
            }
        }
        return dp[m][n];
    }
};

class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix)
    {
        int m = matrix.size();
        int n = matrix[0].size();

        vector<vector<int>> dp(m + 1, vector<int>(n + 2, INT_MAX));

        for (int j = 0; j <= n + 1; ++j)
            dp[0][j] = 0;

        for (int i = 1; i <= m; ++i)
        {
            for (int j = 1; j <= n; ++j)
            {
                dp[i][j] = min(min(dp[i - 1][j - 1], dp[i - 1][j]), dp[i - 1][j + 1]) + matrix[i - 1][j - 1];
            }
        }
        int ret = INT_MAX;
        for (int j = 0; j <= n + 1; ++j)
            ret = min(ret, dp[m][j]);
        return ret;
    }
};

class Solution {
public:
    int calculateMinimumHP(vector<vector<int>>& dungeon)
    {
        int m = dungeon.size();
        int n = dungeon[0].size();

        vector<vector<int>> dp(m + 1, vector<int>(n + 1, INT_MAX));
        dp[m][n - 1] = 1;

        for (int i = m - 1; i >= 0; --i)
        {
            for (int j = n - 1; j >= 0; --j)
            {
                dp[i][j] = min(dp[i][j + 1], dp[i + 1][j]) - dungeon[i][j];
                dp[i][j] = max(1, dp[i][j]);
            }
        }
        return dp[0][0];
    }
};